Evaluating the Effect of Tissue Anisotropy on Brain Tumor Growth using a Mechanically-coupled Reaction-Diffusion Model

Glioblastoma (GBM), the most frequent malignant brain tumor in adults, is char- acterized by rapid growth and healthy tissue invasion. Long-term prognosis for GBM remains poor with median overall survival between 1 y to 2 y [15]. GBM presents with different growth phenotypes, ranging from invasive tumors without notable mass-effect to strongly displacing lesions. Biomechanical forces, such as those resulting from displacive tumor growth, shape the tumor environment and contribute to tumor progression [9]. We present an extended version of a mechanically–coupled reaction-diffusion model of brain tu- mor growth [1] that simulates tumor evolution over time and across different brain regions using literature-based parameter estimates for tumor cell proliferation, as well as isotropic motility, and mechanical tissue properties. This model yielded realistic estimates of the mechanical impact of a growing tumor on intra-cranial pressure. However, comparison to imaging data showed that asymmetric shapes could not be reproduced by isotropic growth assumptions. We modified this model to account for structural tissue anisotropy which is known to affect the directionality of tumor cell migration and may influence the mechanical behavior of brain tissue. Tumors were seeded at multiple locations in a human MR-DTI brain atlas and their spatio-temporal evolution was simulated using the Finite-Element Method. We evaluated the impact of tissue anisotropy on the model’s ability to reproduce the aspherical shapes of real pathologies by comparing predicted lesions to publicly available GBM imaging data. We found the impact on tumor shape to be strongly location dependent and highest for tumors located in brain regions that are characterized by a single dominant white matter direction, such as the corpus callosum. However, despite strongly anisotropic growth assumptions, all simulated tumors remained more spherical than real lesions at the corresponding location and similar volume. This finding is in agreement with previous studies [17, 6] suggesting that anisotropic cell migration along white matter fiber tracks is not a major determinant of tumor shape in the setting of reaction-diffusion based tumor growth models and for most locations across the brain